Last visit was: 12 Aug 2024, 22:32 It is currently 12 Aug 2024, 22:32
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# x and y are positive integers. If the greatest common divisor of 3x

SORT BY:
Tags:
Show Tags
Hide Tags
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30998 [33]
Given Kudos: 799
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30998 [16]
Given Kudos: 799
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11528
Own Kudos [?]: 35116 [8]
Given Kudos: 333
General Discussion
SVP
Joined: 26 Mar 2013
Posts: 2455
Own Kudos [?]: 1375 [1]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
x and y are positive integers. If the greatest common divisor of 3x [#permalink]
1
Kudos
Great question as always.

x and y are positive integers. If the greatest common divisor of 3x and 3y is 6, what is the value of y?

Analyzing the prompt:

GCD of 3x and 3y is 6.......it means that both numbers MUST have 2 in its prime factorization, with one of them with power of 1. By definition GCD consists of prime factors with smallest exponent. For example:

3x=12...x=2^2 & 3y=6...y=2...............GCD=6

3x=6.....x=2 & 3y=12..y=2^2..........GCD=6

3x=12...x=2^2 & 3y=18..y=6..............GCD=6

3x=12...x=2^2 & 3y=30...y=10...........GCD=6 (Notice that 30 has 5 so smallest factor is 5^0 in 12)

(1) The greatest common divisor of 2x and 2y is 2y

Spotting the statement above means that 2x is dividable by 2y.

2x/2y= 2y.......x=2y^2....... it becomes the following:

GCD of 6y^2 & 3y = 6.......There is one solution which is y=2.

Sufficient

(2) The least common multiple of 2x and 2y is 20

20= (2^2) (5)

3x=3*2=6 & 3y=3*2*5=30.........GDC=6.......y=10

3x=3*2*5=30 & 3y=3*2=6...............GCD=6.......y=2

Insufficient

Senior Manager
Joined: 02 Apr 2014
Posts: 369
Own Kudos [?]: 497 [1]
Given Kudos: 1227
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
Re: x and y are positive integers. If the greatest common divisor of 3x [#permalink]
1
Kudos
GCF(3x,3y) = 6 => implies that x = 2m, y = 2n, where m and n are co-primes

Statement 1: GCF(2x, 2y) = 2y => which means y is multiple of x, and this can happen only when y = 2 (n = 1). sufficient
Statement 2: LCM(2x,2y) = 20
I can see two cases, x = 2, y = 2 * 5
or x = 2 * 5 , y = 2
not sufficient

(A)
Retired Moderator
Joined: 19 Oct 2018
Posts: 1868
Own Kudos [?]: 6736 [0]
Given Kudos: 705
Location: India
Re: x and y are positive integers. If the greatest common divisor of 3x [#permalink]
HCF(3x, 3y)=6
therefore HCF(x, y)= 2

Statement 1- HCF of (2x, 2y)= 2y
HCF(x, y)=y
Hence y=2
Sufficient

Statement 2
LCM(2x, 2y)= 20
LCM(x, y)=10
x*y= HCF(x, y)*LCM(x, y)=2*10=20
x and y both are even, hence y can be either 2 or 10
Insufficient

GMATPrepNow wrote:
x and y are positive integers. If the greatest common divisor of 3x and 3y is 6, what is the value of y?

(1) The greatest common divisor of 2x and 2y is 2y
(2) The least common multiple of 2x and 2y is 20

*kudos for all correct solutions
Tutor
Joined: 04 Aug 2010
Posts: 1330
Own Kudos [?]: 3264 [0]
Given Kudos: 9
Schools:Dartmouth College
Re: x and y are positive integers. If the greatest common divisor of 3x [#permalink]
BrentGMATPrepNow wrote:
x and y are positive integers. If the greatest common divisor of 3x and 3y is 6, what is the value of y?

(1) The greatest common divisor of 2x and 2y is 2y
(2) The least common multiple of 2x and 2y is 20

The greatest common divisor of 3x and 3y is 6.
To simplify this statement and isolate x and y, divide every value by 3:
The greatest common divisor of 3x/3 and 3y/3 is 6/3.
In other words:
The greatest common divisor of x and y is 2.

Statement 1:
The greatest common divisor of 2x and 2y is 2y.
To simplify this statement and isolate x and y, divide every value by 2:
The greatest common divisor of 2x/2 and 2y/2 is 2y/2.
In other words:
The greatest common divisor of x and y is y.

Statement 1 indicates that the GCD = y.
The prompt indicates that the GCD = 2.
Thus, y=2.
SUFFICIENT.

Statement 2:
The least common multiple of 2x and 2y is 20
To simplify this statement and isolate x and y, divide every value by 2:
The least common multiple of 2x/2 and 2y/2 is 20/2.
In other words:
The least common multiple of x and y is 10.

Case 1: x=2 and y=10, with the result that the GCD = 2 and the LCM = 10
Case 2: x=10 and y=2, with the result that the GCD = 2 and the LCM = 10
Since y can be different values, INSUFFICIENT.

Intern
Joined: 05 Jul 2022
Posts: 4
Own Kudos [?]: 1 [0]
Given Kudos: 1
Re: x and y are positive integers. If the greatest common divisor of 3x [#permalink]
GMATGuruNY wrote:
BrentGMATPrepNow wrote:
x and y are positive integers. If the greatest common divisor of 3x and 3y is 6, what is the value of y?

(1) The greatest common divisor of 2x and 2y is 2y
(2) The least common multiple of 2x and 2y is 20

The greatest common divisor of 3x and 3y is 6.
To simplify this statement and isolate x and y, divide every value by 3:
The greatest common divisor of 3x/3 and 3y/3 is 6/3.
In other words:
The greatest common divisor of x and y is 2.

Statement 1:
The greatest common divisor of 2x and 2y is 2y.
To simplify this statement and isolate x and y, divide every value by 2:
The greatest common divisor of 2x/2 and 2y/2 is 2y/2.
In other words:
The greatest common divisor of x and y is y.

Statement 1 indicates that the GCD = y.
The prompt indicates that the GCD = 2.
Thus, y=2.
SUFFICIENT.

Statement 2:
The least common multiple of 2x and 2y is 20
To simplify this statement and isolate x and y, divide every value by 2:
The least common multiple of 2x/2 and 2y/2 is 20/2.
In other words:
The least common multiple of x and y is 10.

Case 1: x=2 and y=10, with the result that the GCD = 2 and the LCM = 10
Case 2: x=10 and y=2, with the result that the GCD = 2 and the LCM = 10
Since y can be different values, INSUFFICIENT.

I was wondering, is this linearity of the GCF/LCM operator valid for every such type of relationship?
Non-Human User
Joined: 09 Sep 2013
Posts: 34396
Own Kudos [?]: 862 [0]
Given Kudos: 0
Re: x and y are positive integers. If the greatest common divisor of 3x [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: x and y are positive integers. If the greatest common divisor of 3x [#permalink]
Moderator:
Math Expert
94906 posts